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Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks generated…
Complex network theory aims to model and analyze complex systems that consist of multiple and interdependent components. Among all studies on complex networks, topological structure analysis is of the most fundamental importance, as it…
Using a master-equation approach for the description of coherent and incoherent dynamics in `artificial atoms and molecules', we present a theoretical analysis of situations where intense laser fields lead to pronounced renormalizations of…
We consider weakly interacting jump processes on time-varying random graphs with dynamically changing multi-color edges. The system consists of a large number of nodes in which the node dynamics depends on the joint empirical distribution…
Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…
We argue that chaotic power-law interacting systems have emergent limits on information propagation, analogous to relativistic light cones, which depend on the spatial dimension $d$ and the exponent $\alpha$ governing the decay of…
This chapter aims at reviewing complex networks models and methods that were either developed for or applied to socioeconomic issues, and pertinent to the theme of New Economic Geography. After an introduction to the foundations of the…
The observed scarcity of chaotic phenomena in astronomy contrasts sharply with their theoretical significance, primarily due to the absence of a robust framework for detecting chaos. In this study, we numerically simulate the light curves…
We explore the ability of two-dimensional periodic atom arrays to produce light amplification and generate laser emission when gain is introduced through external optical pumping. Specifically, we predict that lasing can take place for…
While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be…
Spherical and cylindrical dielectric cavities support high Q whispering gallery modes due to total internal reflection of the trapped light. When such a cavity is deformed smoothly the ray dynamics of these modes becomes chaotic in a manner…
This article addresses the problem of reconstructing the topology of a network of agents interacting via linear dynamics, while being excited by exogenous stochastic sources that are possibly correlated across the agents, from time-series…
There has recently been considerable interest in studying quantum systems via dynamical Lie algebras (DLAs) -- Lie algebras generated by the terms which appear in the Hamiltonian of the system. However, there are some important properties…
Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex…
We develop a real-time anomaly detection algorithm for directed activity on large, sparse networks. We model the propensity for future activity using a dynamic logistic model with interaction terms for sender- and receiver-specific latent…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. In particular, we are interested in…
We determine the optimum topology of quasi-one dimensional nonlinear optical structures using generalized quantum graph models. Quantum graphs are relational graphs endowed with a metric and a multiparticle Hamiltonian acting on the edges,…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
Networks observed in the real world often have many short loops. This violates the tree-like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible…